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    "# Introduction to Probability and Statistics\r\n",
    "|\r\n",
    "In this notebook, we will play around with some of the concepts we have previously discussed. Many concepts from probability and statistics are well-represented in major libraries for data processing in Python, such as `numpy` and `pandas`."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "source": [
    "import numpy as np\r\n",
    "import pandas as pd\r\n",
    "import random\r\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "\r\n",
    "## Random Variables and Distributions\r\n",
    "\r\n",
    "Let's start with drawing a sample of 30 variables from a uniform disribution from 0 to 9. We will also compute mean and variance."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "source": [
    "sample = [ random.randint(0,10) for _ in range(30) ]\r\n",
    "print(f\"Sample: {sample}\")\r\n",
    "print(f\"Mean = {np.mean(sample)}\")\r\n",
    "print(f\"Variance = {np.var(sample)}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Sample: [1, 1, 0, 5, 6, 3, 7, 5, 1, 6, 5, 6, 7, 0, 3, 6, 2, 4, 2, 8, 1, 5, 7, 10, 8, 5, 7, 10, 6, 8]\n",
      "Mean = 4.833333333333333\n",
      "Variance = 7.938888888888889\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "To visually estimate how many different values are there in the sample, we can plot the **histogram**:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "source": [
    "plt.hist(sample)\r\n",
    "plt.show()"
   ],
   "outputs": [
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Analyzing Real Data\r\n",
    "\r\n",
    "Mean and variance are very important when analyzing real-world data. Let's load the data about baseball players from [SOCR MLB Height/Weight Data](http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_MLB_HeightsWeights)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "source": [
    "df = pd.read_csv(\"../../data/SOCR_MLB.tsv\",sep='\\t',header=None,names=['Name','Team','Role','Height','Weight','Age'])\r\n",
    "df"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "                 Name Team            Role  Height  Weight    Age\n",
       "0       Adam_Donachie  BAL         Catcher      74   180.0  22.99\n",
       "1           Paul_Bako  BAL         Catcher      74   215.0  34.69\n",
       "2     Ramon_Hernandez  BAL         Catcher      72   210.0  30.78\n",
       "3        Kevin_Millar  BAL   First_Baseman      72   210.0  35.43\n",
       "4         Chris_Gomez  BAL   First_Baseman      73   188.0  35.71\n",
       "...               ...  ...             ...     ...     ...    ...\n",
       "1029    Brad_Thompson  STL  Relief_Pitcher      73   190.0  25.08\n",
       "1030    Tyler_Johnson  STL  Relief_Pitcher      74   180.0  25.73\n",
       "1031   Chris_Narveson  STL  Relief_Pitcher      75   205.0  25.19\n",
       "1032    Randy_Keisler  STL  Relief_Pitcher      75   190.0  31.01\n",
       "1033      Josh_Kinney  STL  Relief_Pitcher      73   195.0  27.92\n",
       "\n",
       "[1034 rows x 6 columns]"
      ],
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Team</th>\n",
       "      <th>Role</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Adam_Donachie</td>\n",
       "      <td>BAL</td>\n",
       "      <td>Catcher</td>\n",
       "      <td>74</td>\n",
       "      <td>180.0</td>\n",
       "      <td>22.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Paul_Bako</td>\n",
       "      <td>BAL</td>\n",
       "      <td>Catcher</td>\n",
       "      <td>74</td>\n",
       "      <td>215.0</td>\n",
       "      <td>34.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Ramon_Hernandez</td>\n",
       "      <td>BAL</td>\n",
       "      <td>Catcher</td>\n",
       "      <td>72</td>\n",
       "      <td>210.0</td>\n",
       "      <td>30.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Kevin_Millar</td>\n",
       "      <td>BAL</td>\n",
       "      <td>First_Baseman</td>\n",
       "      <td>72</td>\n",
       "      <td>210.0</td>\n",
       "      <td>35.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Chris_Gomez</td>\n",
       "      <td>BAL</td>\n",
       "      <td>First_Baseman</td>\n",
       "      <td>73</td>\n",
       "      <td>188.0</td>\n",
       "      <td>35.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1029</th>\n",
       "      <td>Brad_Thompson</td>\n",
       "      <td>STL</td>\n",
       "      <td>Relief_Pitcher</td>\n",
       "      <td>73</td>\n",
       "      <td>190.0</td>\n",
       "      <td>25.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1030</th>\n",
       "      <td>Tyler_Johnson</td>\n",
       "      <td>STL</td>\n",
       "      <td>Relief_Pitcher</td>\n",
       "      <td>74</td>\n",
       "      <td>180.0</td>\n",
       "      <td>25.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1031</th>\n",
       "      <td>Chris_Narveson</td>\n",
       "      <td>STL</td>\n",
       "      <td>Relief_Pitcher</td>\n",
       "      <td>75</td>\n",
       "      <td>205.0</td>\n",
       "      <td>25.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1032</th>\n",
       "      <td>Randy_Keisler</td>\n",
       "      <td>STL</td>\n",
       "      <td>Relief_Pitcher</td>\n",
       "      <td>75</td>\n",
       "      <td>190.0</td>\n",
       "      <td>31.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1033</th>\n",
       "      <td>Josh_Kinney</td>\n",
       "      <td>STL</td>\n",
       "      <td>Relief_Pitcher</td>\n",
       "      <td>73</td>\n",
       "      <td>195.0</td>\n",
       "      <td>27.92</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1034 rows × 6 columns</p>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "execution_count": 215
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "> We are using a package called **Pandas** here for data analysis. We will talk more about Pandas and working with data in Python later in this course.\r\n",
    "\r\n",
    "Let's compute average values for age, height and weight:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "source": [
    "df[['Age','Height','Weight']].mean()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Age        28.736712\n",
       "Height     73.697292\n",
       "Weight    201.689255\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "execution_count": 216
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now let's focus on height, and compute standard deviation and variance: "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "source": [
    "print(list(df['Height'])[:20])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[180.0, 215.0, 210.0, 210.0, 188.0, 176.0, 209.0, 200.0, 231.0, 180.0, 188.0, 180.0, 185.0, 160.0, 180.0, 185.0, 197.0, 189.0, 185.0, 219.0]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "source": [
    "mean = df['Height'].mean()\r\n",
    "var = df['Height'].var()\r\n",
    "std = df['Height'].std()\r\n",
    "print(f\"Mean = {mean}\\nVariance = {var}\\nStandard Deviation = {std}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Mean = 73.6972920696325\n",
      "Variance = 5.316798081118081\n",
      "Standard Deviation = 2.305818310517566\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "In addition to mean, it makes sense to look at median value and quartiles. They can be visualized using **box plot**:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "source": [
    "plt.figure(figsize=(10,2))\r\n",
    "plt.boxplot(df['Height'],vert=False,showmeans=True)\r\n",
    "plt.grid(color='gray',linestyle='dotted')\r\n",
    "plt.show()"
   ],
   "outputs": [
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can also make box plots of subsets of our dataset, for example, grouped by player role."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "source": [
    "df.boxplot(column='Height',by='Role')\r\n",
    "plt.xticks(rotation='vertical')\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "> **Note**: This diagram suggests, that on average, height of first basemen is higher that height of second basemen. Later we will learn how we can test this hypothesis more formally, and how to demonstrate that our data is statistically significant to show that.  \r\n",
    "\r\n",
    "Age, height and weight are all continuous random variables. What do you think their distribution is? A good way to find out is to plot the histogram of values: "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "source": [
    "df['Weight'].hist(bins=15)\r\n",
    "plt.suptitle('Weight distribution of MLB Players')\r\n",
    "plt.xlabel('Weight')\r\n",
    "plt.ylabel('Count')\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Normal Distribution\r\n",
    "\r\n",
    "Let's create an artificial sample of weights that follows normal distribution with the same mean and variance as real data:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "source": [
    "generated = np.random.normal(mean,std,1000)\r\n",
    "generated[:20]"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([187.05660174, 181.77292853, 183.09148457, 198.30703945,\n",
       "       201.51640234, 213.21564624, 221.00562653, 218.30263433,\n",
       "       234.16968198, 187.40138853, 199.34286071, 205.52705493,\n",
       "       251.03651986, 189.64156046, 222.23536452, 211.37502445,\n",
       "       205.07287496, 207.90248813, 180.66579133, 226.86092236])"
      ]
     },
     "metadata": {},
     "execution_count": 60
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "source": [
    "plt.hist(generated,bins=15)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "source": [
    "plt.hist(np.random.normal(0,1,50000),bins=300)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
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      ],
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5ecrLy1N5eblGjBihhQsXSpLcbrcWL16sFStWaPTo0Ro1apRWrlypiRMnqri4eEh2EAAuh47LjU+tm+1wJUBiiCqgfPzxx3rggQfU2Ngot9utSZMm6bXXXtOMGTMkSatWrVJra6uWLl2qpqYmFRYWav/+/crKyrJ/xsaNG5WamqoFCxaotbVV06dP186dO5WSkhLbPQMMw/0yAKD/XJZlWU4XEa1QKCS3261gMMh8FBhrwup9EZ+mCSiJ69S62XRQgH6I5u83XxYIDCHuNAoAA0NAAYAYI5gCg0dAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFuAy45BQAokNAAQAAxiGgAMAg0SEDYo+AAgAAjENAAWKAW5sDQGwRUAAAgHEIKAAQQ3TSgNggoAAAAOMQUABgiNBNAQaOgAIMEBNjAWDopDpdAJBoCC0AMHh0UIBBIpAAQOwRUAAAgHEIKEAM0U1BV53nKjFvCeg/AgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgCXAbe4B6JDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgA4YMLqfVzZA/SBgAIAAIxDQAEAAMYhoACX0LkVT1seAC4PAgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUADgMuNKMODSCCgAAMA4BBRgAPgEDABDi4ACAACME1VAqaio0K233qqsrCyNHTtW8+bN07vvvhsxxrIslZWVyefzKSMjQ0VFRTpx4kTEmHA4rNLSUo0ZM0aZmZmaO3euzpw5M/i9AWKMTgmGWud/Y/x7A/4nqoBSU1OjZcuW6fDhw6qurtbnn3+ukpISXbhwwR6zfv16bdiwQVu2bNGRI0fk9Xo1Y8YMNTc322P8fr+qqqpUWVmpgwcPqqWlRXPmzFF7e3vs9gyIMf54AMDl47Isyxrokz/55BONHTtWNTU1uv3222VZlnw+n/x+vx599FFJ/+2WeDwe/eIXv9BDDz2kYDCoq666Srt379Y999wjSTp79qxycnL0yiuvaObMmZf8vaFQSG63W8FgUNnZ2QMtH7gkQgkut1PrZjtdAjBkovn7Pag5KMFgUJI0atQoSdLJkycVCARUUlJij0lPT9e0adN06NAhSVJtba0uXrwYMcbn8yk/P98e01U4HFYoFIpYAABA4hpwQLEsS8uXL9dtt92m/Px8SVIgEJAkeTyeiLEej8feFggElJaWppEjR/Y6pquKigq53W57ycnJGWjZAAAgDgw4oDz88MN6++239fzzz3fb5nK5Ih5bltVtXVd9jVmzZo2CwaC9NDQ0DLRsADDahNX7OLUIaIABpbS0VH/605/0t7/9TePGjbPXe71eSerWCTl37pzdVfF6vWpra1NTU1OvY7pKT09XdnZ2xAIAABJXVAHFsiw9/PDD+uMf/6i//vWvys3Njdiem5srr9er6upqe11bW5tqamo0depUSVJBQYGGDRsWMaaxsVH19fX2GAAAkNxSoxm8bNky7d27Vy+//LKysrLsTonb7VZGRoZcLpf8fr/Ky8uVl5envLw8lZeXa8SIEVq4cKE9dvHixVqxYoVGjx6tUaNGaeXKlZo4caKKi4tjv4cAACDuRBVQtm3bJkkqKiqKWP/ss89q0aJFkqRVq1aptbVVS5cuVVNTkwoLC7V//35lZWXZ4zdu3KjU1FQtWLBAra2tmj59unbu3KmUlJTB7Q0AAEgIg7oPilO4DwouFyYrwincDwWJ6LLdBwVIRIQSAHAeAQUAABiHgAIAAIxDQAEAAMYhoACA4ZgXhWREQAEAAMYhoAAAAONEdaM2IJF1bqPTUocJ+HeIZEYHBQAAGIeAAgAAjENAAQADcXoHyY6AAgAAjENAAQAAxiGgAAAA4xBQAACAcQgogJiQCPNNWL2Pf6dIKtyoDUmNAz4AmIkOCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgIOlwNQQAmI+AAgAAjENAAQAAxiGgAEAc4fQkkgUBBQAAGIeAgqTFJ1EAMBcBBQDiFCEbiYyAAgAAjENAAQAAxiGgAAAA4xBQACDO9HU3ZOalIFEQUAAAgHEIKAAQx/huKSQqAgoAADAOAQVJhU+aABAfCChIGF3DB61vAIhfBBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQEFC6jw5lomyABB/CCgAAMA4BBQAAGCcVKcLAAAMHqcykWjooAAAAOPQQUFS4NMlAMQXOigAAMA4BBQkFL5/B/gf3guIZ5ziAYAEQzBBIoi6g/Lmm2/qzjvvlM/nk8vl0ksvvRSx3bIslZWVyefzKSMjQ0VFRTpx4kTEmHA4rNLSUo0ZM0aZmZmaO3euzpw5M6gdAQD0jtCCeBN1QLlw4YJuvPFGbdmypcft69ev14YNG7RlyxYdOXJEXq9XM2bMUHNzsz3G7/erqqpKlZWVOnjwoFpaWjRnzhy1t7cPfE8AAEDCiPoUz6xZszRr1qwet1mWpU2bNmnt2rWaP3++JGnXrl3yeDzau3evHnroIQWDQe3YsUO7d+9WcXGxJGnPnj3KycnRgQMHNHPmzEHsDgDgUias3qdT62Y7XQbQp5hOkj158qQCgYBKSkrsdenp6Zo2bZoOHTokSaqtrdXFixcjxvh8PuXn59tjAACxwcRxxKuYTpINBAKSJI/HE7He4/Howw8/tMekpaVp5MiR3cZ0PL+rcDiscDhsPw6FQrEsGwAAGGZILjN2uVwRjy3L6rauq77GVFRUyO1220tOTk7MagUAAOaJaUDxer2S1K0Tcu7cObur4vV61dbWpqampl7HdLVmzRoFg0F7aWhoiGXZiEO0rQEgscU0oOTm5srr9aq6utpe19bWppqaGk2dOlWSVFBQoGHDhkWMaWxsVH19vT2mq/T0dGVnZ0csAIDoEOwRT6IOKC0tLaqrq1NdXZ2k/06Mraur0+nTp+VyueT3+1VeXq6qqirV19dr0aJFGjFihBYuXChJcrvdWrx4sVasWKHXX39dx44d0/3336+JEyfaV/UA/cXBFogd3k8wSdSTZI8ePao77rjDfrx8+XJJ0oMPPqidO3dq1apVam1t1dKlS9XU1KTCwkLt379fWVlZ9nM2btyo1NRULViwQK2trZo+fbp27typlJSUGOwSAACIdy7Lsiyni4hWKBSS2+1WMBjkdE+S4pMeMDg93QeF+6NgqEXz95svC0TcIZwAscP7CaYioAAAAOPwbcYAkITonMB0dFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgIK4wBUHAJBcCCgAgG74UACnEVAAAIBxCCgAAMA4BBQYhbYyAEDiVvcAkPT4YAAT0UEBAADGoYMCY/GpDjDDhNX7dGrdbKfLQJIhoMAIhBEAQGec4gEAAMahgwLj9NZNocsCDD3eZzAFHRQ4ZsLqfRwMAQA9IqAAAADjEFAAAIBxmIMCx3GaB4gfnd+vXHqMoUQHBQAAGIeAAgAYMCa7Y6gQUAAAgHGYgwIA6FHnzkhPXRI6JxhKdFAwJGj7AgAGg4CCy+ZSn8YAAOhAQAEAxBxdVAwWAQWXFQctIDHxvkasMUkWQ44DFwAgWnRQAABDqnPnlC4q+ouAgqhxgAHQF44PiAUCCmKG4AIAiBUCCgDgsuBWA4gGAQUxx0EIADBYBBQMGOEDQGc9neblOIGBIqDgkvo6wDDvBAAwFAgoAABH8SEHPSGgAAAA43AnWQCAI+icoC90UAAAxiC0oAMBBb1iAiwAJ3H8SW4EFESltwMGBxIAgxHNByLutZQcmIMCADAWASR5EVAAAEYhlEDiFE/Si6alykEDgOk4ViUOOihJoOPNemrd7G7rum7njQ0gHvR0rOL4lVjooAAAEhLdlPhGByWJXOqNyhsZQDyK5tg1YfW+iG4yzOVoB2Xr1q3Kzc3V8OHDVVBQoLfeesvJcowVbXAgaADA/3R0Uvim5fjiWAflhRdekN/v19atW/XNb35TTz/9tGbNmqV33nlH48ePd6qsmOtp/kc0z+vpccfP6mndpX4OACSDgRz7Bnq8xtBwWZZlOfGLCwsLdcstt2jbtm32uuuuu07z5s1TRUVFn88NhUJyu90KBoPKzs4e6lL7pbd/2Jf6B99byOjrzdVTQAEADFxvFwkQVmIrmr/fjnRQ2traVFtbq9WrV0esLykp0aFDh7qND4fDCofD9uNgMCjpvzs6FPIf/4vqfzaz122Sum3/IvyZXVPnMR3rx//fixHP6RjT2fj/e7Ff9XXsd8fPBgAMTigU6vGY2vXvTE/H7s7qfzYzYkzHcb+vvys9iXZ8vOj4/9mv3ojlgI8++siSZP3973+PWP/kk09a1157bbfxjz/+uCWJhYWFhYWFJQGWhoaGS2YFR6/icblcEY8ty+q2TpLWrFmj5cuX24+/+OIL/ec//9Ho0aN7HN+TUCiknJwcNTQ0GHNaCJfG6xafeN3iE69bfIqn182yLDU3N8vn811yrCMBZcyYMUpJSVEgEIhYf+7cOXk8nm7j09PTlZ6eHrHuS1/60oB+d3Z2tvEvILrjdYtPvG7xidctPsXL6+Z2u/s1zpHLjNPS0lRQUKDq6uqI9dXV1Zo6daoTJQEAAIM4dopn+fLleuCBBzR58mRNmTJF27dv1+nTp7VkyRKnSgIAAIZwLKDcc889+vTTT/XEE0+osbFR+fn5euWVV3T11VcPye9LT0/X448/3u1UEczG6xafeN3iE69bfErU182x+6AAAAD0hi8LBAAAxiGgAAAA4xBQAACAcQgoAADAOEkfUMLhsG666Sa5XC7V1dU5XQ56cerUKS1evFi5ubnKyMjQNddco8cff1xtbW1Ol4YebN26Vbm5uRo+fLgKCgr01ltvOV0S+lBRUaFbb71VWVlZGjt2rObNm6d3333X6bIQhYqKCrlcLvn9fqdLiZmkDyirVq3q1y134ax//etf+uKLL/T000/rxIkT2rhxo37729/qsccec7o0dPHCCy/I7/dr7dq1OnbsmL71rW9p1qxZOn36tNOloRc1NTVatmyZDh8+rOrqan3++ecqKSnRhQsXnC4N/XDkyBFt375dkyZNcrqUmErqy4xfffVVLV++XH/4wx90ww036NixY7rpppucLgv99Mtf/lLbtm3TBx984HQp6KSwsFC33HKLtm3bZq+77rrrNG/ePFVUVDhYGfrrk08+0dixY1VTU6Pbb7/d6XLQh5aWFt1yyy3aunWrfv7zn+umm27Spk2bnC4rJpK2g/Lxxx/rJz/5iXbv3q0RI0Y4XQ4GIBgMatSoUU6XgU7a2tpUW1urkpKSiPUlJSU6dOiQQ1UhWsFgUJJ4f8WBZcuWafbs2SouLna6lJhz9NuMnWJZlhYtWqQlS5Zo8uTJOnXqlNMlIUr//ve/tXnzZj311FNOl4JOzp8/r/b29m5f+unxeLp9OSjMZFmWli9frttuu035+flOl4M+VFZWqra2VkePHnW6lCGRUB2UsrIyuVyuPpejR49q8+bNCoVCWrNmjdMlJ73+vmadnT17Vt/5znf0gx/8QD/+8Y8dqhx9cblcEY8ty+q2DmZ6+OGH9fbbb+v55593uhT0oaGhQY888oiee+45DR8+3OlyhkRCzUE5f/68zp8/3+eYCRMm6N5779Wf//zniANme3u7UlJSdN9992nXrl1DXSr+v/6+Zh1vwLNnz+qOO+5QYWGhdu7cqSuuSKiMHffa2to0YsQIvfjii7r77rvt9Y888ojq6upUU1PjYHW4lNLSUr300kt68803lZub63Q56MNLL72ku+++WykpKfa69vZ2uVwuXXHFFQqHwxHb4lFCBZT+On36tEKhkP347Nmzmjlzpn7/+9+rsLBQ48aNc7A69Oajjz7SHXfcoYKCAu3Zsyfu33yJqrCwUAUFBdq6dau97vrrr9ddd93FJFlDWZal0tJSVVVV6Y033lBeXp7TJeESmpub9eGHH0as+9GPfqSvf/3revTRRxPi9FxSzkEZP358xOMrr7xSknTNNdcQTgx19uxZFRUVafz48frVr36lTz75xN7m9XodrAxdLV++XA888IAmT56sKVOmaPv27Tp9+rSWLFnidGnoxbJly7R37169/PLLysrKsucLud1uZWRkOFwdepKVldUthGRmZmr06NEJEU6kJA0oiD/79+/X+++/r/fff79biEzCJqDR7rnnHn366ad64okn1NjYqPz8fL3yyiu6+uqrnS4Nvei4JLyoqChi/bPPPqtFixZd/oIAJekpHgAAYDZmGAIAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgnP8H89I+mMR4d+MAAAAASUVORK5CYII="
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Since most values in real life are normally distributed, it means we should not use uniform random number generator to generate sample data. Here is what happens if we try to generate weights with uniform distribution (generated by `np.random.rand`):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "source": [
    "wrong_sample = np.random.rand(1000)*2*std+mean-std\r\n",
    "plt.hist(wrong_sample)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Confidence Intervals\r\n",
    "\r\n",
    "Let's now calculate confidence intervals for the weights and heights of baseball players. We will use the code [from this stackoverflow discussion](https://stackoverflow.com/questions/15033511/compute-a-confidence-interval-from-sample-data):"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "source": [
    "import scipy.stats\r\n",
    "\r\n",
    "def mean_confidence_interval(data, confidence=0.95):\r\n",
    "    a = 1.0 * np.array(data)\r\n",
    "    n = len(a)\r\n",
    "    m, se = np.mean(a), scipy.stats.sem(a)\r\n",
    "    h = se * scipy.stats.t.ppf((1 + confidence) / 2., n-1)\r\n",
    "    return m, h\r\n",
    "\r\n",
    "for p in [0.85, 0.9, 0.95]:\r\n",
    "    m, h = mean_confidence_interval(df['Weight'].fillna(method='pad'),p)\r\n",
    "    print(f\"p={p:.2f}, mean = {m:.2f}±{h:.2f}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "p=0.85, mean = 201.73±0.94\n",
      "p=0.90, mean = 201.73±1.08\n",
      "p=0.95, mean = 201.73±1.28\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Hypothesis Testing\r\n",
    "\r\n",
    "Let's explore different roles in our baseball players dataset:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "source": [
    "df.groupby('Role').agg({ 'Height' : 'mean', 'Weight' : 'mean', 'Age' : 'count'}).rename(columns={ 'Age' : 'Count'})"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "                      Height      Weight  Count\n",
       "Role                                           \n",
       "Catcher            72.723684  204.328947     76\n",
       "Designated_Hitter  74.222222  220.888889     18\n",
       "First_Baseman      74.000000  213.109091     55\n",
       "Outfielder         73.010309  199.113402    194\n",
       "Relief_Pitcher     74.374603  203.517460    315\n",
       "Second_Baseman     71.362069  184.344828     58\n",
       "Shortstop          71.903846  182.923077     52\n",
       "Starting_Pitcher   74.719457  205.163636    221\n",
       "Third_Baseman      73.044444  200.955556     45"
      ],
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Count</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Role</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Catcher</th>\n",
       "      <td>72.723684</td>\n",
       "      <td>204.328947</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Designated_Hitter</th>\n",
       "      <td>74.222222</td>\n",
       "      <td>220.888889</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>First_Baseman</th>\n",
       "      <td>74.000000</td>\n",
       "      <td>213.109091</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Outfielder</th>\n",
       "      <td>73.010309</td>\n",
       "      <td>199.113402</td>\n",
       "      <td>194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Relief_Pitcher</th>\n",
       "      <td>74.374603</td>\n",
       "      <td>203.517460</td>\n",
       "      <td>315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Second_Baseman</th>\n",
       "      <td>71.362069</td>\n",
       "      <td>184.344828</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Shortstop</th>\n",
       "      <td>71.903846</td>\n",
       "      <td>182.923077</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Starting_Pitcher</th>\n",
       "      <td>74.719457</td>\n",
       "      <td>205.163636</td>\n",
       "      <td>221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Third_Baseman</th>\n",
       "      <td>73.044444</td>\n",
       "      <td>200.955556</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "execution_count": 175
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's test the hypothesis that First Basemen are higher then Second Basemen. The simplest way to do it is to test the confidence intervals:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "source": [
    "for p in [0.85,0.9,0.95]:\r\n",
    "    m1, h1 = mean_confidence_interval(df.loc[df['Role']=='First_Baseman',['Height']],p)\r\n",
    "    m2, h2 = mean_confidence_interval(df.loc[df['Role']=='Second_Baseman',['Height']],p)\r\n",
    "    print(f'Conf={p:.2f}, 1st basemen height: {m1-h1[0]:.2f}..{m1+h1[0]:.2f}, 2nd basemen height: {m2-h2[0]:.2f}..{m2+h2[0]:.2f}')"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Conf=0.85, 1st basemen height: 73.62..74.38, 2nd basemen height: 71.04..71.69\n",
      "Conf=0.90, 1st basemen height: 73.56..74.44, 2nd basemen height: 70.99..71.73\n",
      "Conf=0.95, 1st basemen height: 73.47..74.53, 2nd basemen height: 70.92..71.81\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can see that intervals do not overlap.\r\n",
    "\r\n",
    "More statistically correct way to prove the hypothesis is to use **Student t-test**:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "source": [
    "from scipy.stats import ttest_ind\r\n",
    "\r\n",
    "tval, pval = ttest_ind(df.loc[df['Role']=='First_Baseman',['Height']], df.loc[df['Role']=='Second_Baseman',['Height']],equal_var=False)\r\n",
    "print(f\"T-value = {tval[0]:.2f}\\nP-value: {pval[0]}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "T-value = 7.65\n",
      "P-value: 9.137321189738925e-12\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Two values returned by the `ttest_ind` functions are:\r\n",
    "* p-value can be considered as the probability of two distributions having the same mean. In our case, it is very low, meaning that there is strong evidence supporting that first basemen are taller\r\n",
    "* t-value is the intermediate value of normalized mean difference that is used in t-test, and it is compared against threshold value for a given confidence value "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Simulating Normal Distribution with Central Limit Theorem\r\n",
    "\r\n",
    "Pseudo-random generator in Python is designed to give us uniform distribution. If we want to create a generator for normal distribution, we can use central limit theorem. To get a normally distributed value we will just compute a mean of a uniform-generated sample."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "source": [
    "def normal_random(sample_size=100):\r\n",
    "    sample = [random.uniform(0,1) for _ in range(sample_size) ]\r\n",
    "    return sum(sample)/sample_size\r\n",
    "\r\n",
    "sample = [normal_random() for _ in range(100)]\r\n",
    "plt.hist(sample)\r\n",
    "plt.show()"
   ],
   "outputs": [
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     "output_type": "display_data",
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Correlation and Evil Baseball Corp\r\n",
    "\r\n",
    "Correlation allows us to find inner connection between data sequences. In our toy example, let's pretend there is an evil baseball corporation that pays it's players according to their height - the taller the player is, the more money he/she gets. Suppose there is a base salary of $1000, and an additional bonus from $0 to $100, depending on height. We will take the real players from MLB, and compute their imaginary salaries:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "source": [
    "heights = df['Height']\r\n",
    "salaries = 1000+(heights-heights.min())/(heights.max()-heights.mean())*100\r\n",
    "print(list(zip(heights,salaries))[:10])"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[(74, 1075.2469071629068), (74, 1075.2469071629068), (72, 1053.7477908306478), (72, 1053.7477908306478), (73, 1064.4973489967772), (69, 1021.4991163322591), (69, 1021.4991163322591), (71, 1042.9982326645181), (76, 1096.746023495166), (71, 1042.9982326645181)]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's now compute covariance and correlation of those sequences. `np.cov` will give us so-called **covariance matrix**, which is an extension of covariance to multiple variables. The element $M_{ij}$ of the covariance matrix $M$ is a correlation between input variables $X_i$ and $X_j$, and diagonal values $M_{ii}$ is the variance of $X_{i}$. Similarly, `np.corrcoef` will give us **correlation matrix**."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "source": [
    "print(f\"Covariance matrix:\\n{np.cov(heights,salaries)}\")\r\n",
    "print(f\"Covariance = {np.cov(heights,salaries)[0,1]}\")\r\n",
    "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Covariance matrix:\n",
      "[[  5.31679808  57.15323023]\n",
      " [ 57.15323023 614.37197275]]\n",
      "Covariance = 57.15323023054467\n",
      "Correlation = 1.0\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Correlation equal to 1 means that there is a strong **linear relation** between two variables. We can visually see the linear relation by plotting one value against the other:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "source": [
    "plt.scatter(heights,salaries)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
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     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's see what happens if the relation is not linear. Suppose that our corporation decided to hide the obvious linear dependency between heights and salaries, and introduced some non-linearity into the formula, such as `sin`:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "source": [
    "salaries = 1000+np.sin((heights-heights.min())/(heights.max()-heights.mean()))*100\r\n",
    "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Correlation = 0.9835304456670811\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "In this case, the correlation is slightly smaller, but it is still quite high. Now, to make the relation even less obvious, we might want to add some extra randomness by adding some random variable to the salary. Let's see what happens:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "source": [
    "salaries = 1000+np.sin((heights-heights.min())/(heights.max()-heights.mean()))*100+np.random.random(size=len(heights))*20-10\r\n",
    "print(f\"Correlation = {np.corrcoef(heights,salaries)[0,1]}\")"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Correlation = 0.9384710733057905\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "source": [
    "plt.scatter(heights, salaries)\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
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"
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "> Can you guess why the dots line up into vertical lines like this?\r\n",
    "\r\n",
    "We have observed the correlation between artificially engineered concept like salary and the observed variable *height*. Let's also see if the two observed variables, such as height and weight, also correlate:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "source": [
    "np.corrcoef(df['Height'],df['Weight'])"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1., nan],\n",
       "       [nan, nan]])"
      ]
     },
     "metadata": {},
     "execution_count": 111
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Unfortunately, we did not get any results - only some strange `nan` values. This is due to the fact that some of the values in our series are undefined, represented as `nan`, which causes the result of the operation to be undefined as well. By looking at the matrix we can see that `Weight` is problematic column, because self-correlation between `Height` values has been computed.\r\n",
    "\r\n",
    "> This example shows the importance of **data preparation** and **cleaning**. Without proper data we cannot compute anything.\r\n",
    "\r\n",
    "Let's use `fillna` method to fill the missing values, and compute the correlation: "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "source": [
    "np.corrcoef(df['Height'],df['Weight'].fillna(method='pad'))"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[1.        , 0.52959196],\n",
       "       [0.52959196, 1.        ]])"
      ]
     },
     "metadata": {},
     "execution_count": 114
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The is indeed a correlation, but not such a strong one as in our artificial example. Indeed, if we look at the scatter plot of one value against the other, the relation would be much less obvious:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "source": [
    "plt.scatter(df['Height'],df['Weight'])\r\n",
    "plt.xlabel('Height')\r\n",
    "plt.ylabel('Weight')\r\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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"
     },
     "metadata": {}
    }
   ],
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  },
  {
   "cell_type": "markdown",
   "source": [
    "## Conclusion\r\n",
    "\r\n",
    "In this notebook, we have learnt how to perform basic operations on data to compute statistical functions. We now know how to use sound apparatus of math and statistics in order to prove some hypotheses, and how to compute confidence intervals for random variable given data sample. "
   ],
   "metadata": {}
  }
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